Pseudo Empirical Best Prediction of Multiple Characteristics in Small Areas

Abstract

Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under unit-level models typically focus on a single response variable. This paper addresses the estimation of area means for several dependent target variables under a multivariate nested error regression (MNER) model. We propose a multivariate pseudo-empirical best linear unbiased predictor that accounts for the sampling mechanism. Moreover, by aggregating the MNER model, we derive a unified predictor that can be obtained from either unit-level or area-level data. Bootstrap procedures are proposed to estimate the mean squared errors (MSEs) of the proposed predictors. Simulation experiments are conducted to examine the properties of the proposed small area estimators and the MSE estimators. Finally, an application with housing data illustrates the proposed methods.

Figures (8)

• Figure 1: % RB of DIR, MFH, MYR and UYR, for $d=1,\ldots, D$, for $r=1$ (above) and $r=2$ (below).
• Figure 2: % RRMSE of DIR, MFH, MYR and UYR for each area $d=1,\ldots,D$, for $r=1$ (above) and $r=2$ (below).
• Figure 3: True values of $\hbox{MSE}(\hat{\mu}^{MYR}_{dr})$ and MC averages of PB MSE estimator, $\hbox{mse}_{PB}(\hat{\mu}^{MYR}_{dr})$, for each area $d=1,\ldots,D$, for $r=1$ (above) and $r=2$ (below).
• Figure 4: Bivariate Normal Q-Q plot of predicted area effects (A) and Bivariate Normal Q-Q plot of unit-level residuals from BNER model (B).
• Figure 5: DIR, MFH, MYR and UYR estimators of the means of MRC and MP by department and household type, presented in ascending order of sample size.